Neural network representation and learning of mappings and their derivatives

Discussed here are recent theorems proving that artificial neural networks are capable of approximating an arbitrary mapping and its derivatives as accurately as desired. This fact forms the basis for further results establishing the learnability of the desired approximations, using results from non-parametric statistics. These results have potential applications in robotics, chaotic dynamics, control, and sensitivity analysis. An example involving learning the transfer function and its derivatives for a chaotic map is discussed

Functional Multi-Layer Perceptron: a Nonlinear Tool for Functional Data Analysis

In this paper, we study a natural extension of Multi-Layer Perceptrons (MLP) to functional inputs. We show that fundamental results for classical MLP can be extended to functional MLP. We obtain universal approximation results that show the expressive power of functional MLP is comparable to that of numerical MLP. We obtain consistency results which imply that the estimation of optimal parameters for functional MLP is statistically well defined. We finally show on simulated and real world data that the proposed model performs in a very satisfactory way.Comment: http://www.sciencedirect.com/science/journal/0893608

Sequentially testing polynomial model hypotheses using power transforms of regressors

We provide a methodology for testing a polynomial model hypothesis by generalizing the approach and results of Baek, Cho, and Phillips (Journal of Econometrics, 2015, 187, 376–384; BCP), which test for neglected nonlinearity using power transforms of regressors against arbitrary nonlinearity. We use the BCP quasi-likelihood ratio test and deal with the new multifold identification problem that arises under the null of the polynomial model. The approach leads to convenient asymptotic theory for inference, has omnibus power against general nonlinear alternatives, and allows estimation of an unknown polynomial degree in a model by way of sequential testing, a technique that is useful in the application of sieve approximations. Simulations show good performance in the sequential test procedure in both identifying and estimating unknown polynomial order. The approach, which can be used empirically to test for misspecification, is applied to a Mincer (Journal of Political Economy, 1958, 66, 281–302; Schooling, Experience and Earnings, Columbia University Press, 1974) equation using data from Card (in Christofides, Grant, and Swidinsky (Eds.), Aspects of Labour Market Behaviour: Essays in Honour of John Vanderkamp, University of Toronto Press, 1995, 201-222) and Bierens and Ginther (Empirical Economics, 2001, 26, 307–324). The results confirm that the standard Mincer log earnings equation is readily shown to be misspecified. The applications consider different datasets and examine the impact of nonlinear effects of experience and schooling on earnings, allowing for flexibility in the respective polynomial representations

Theoretical Properties of Projection Based Multilayer Perceptrons with Functional Inputs

Many real world data are sampled functions. As shown by Functional Data Analysis (FDA) methods, spectra, time series, images, gesture recognition data, etc. can be processed more efficiently if their functional nature is taken into account during the data analysis process. This is done by extending standard data analysis methods so that they can apply to functional inputs. A general way to achieve this goal is to compute projections of the functional data onto a finite dimensional sub-space of the functional space. The coordinates of the data on a basis of this sub-space provide standard vector representations of the functions. The obtained vectors can be processed by any standard method. In our previous work, this general approach has been used to define projection based Multilayer Perceptrons (MLPs) with functional inputs. We study in this paper important theoretical properties of the proposed model. We show in particular that MLPs with functional inputs are universal approximators: they can approximate to arbitrary accuracy any continuous mapping from a compact sub-space of a functional space to R. Moreover, we provide a consistency result that shows that any mapping from a functional space to R can be learned thanks to examples by a projection based MLP: the generalization mean square error of the MLP decreases to the smallest possible mean square error on the data when the number of examples goes to infinity

Organization Theory in Business and Management History: Present Status and Future Prospects

Copyright © The President and Fellows of Harvard College 2017. A common lament is that business history has been marginalized within mainstream business and management research. We propose that the remedy lies in part with more extensive engagement with organization theory. We illustrate our argument by exploring the potentialities for business history of three cognitive frameworks: institutional entrepreneurship, evolutionary theory, and Bourdieusian social theory. Exhibiting a higher level of theoretical fluency might enable business historians to accrue scholarly capital within the business and management field by producing theoretically informed historical discourse, demonstrating the potential of business history to extend theory, generate constructs, and elucidate complexities in unfolding relationships, situations, and events

Fluctuating Viability Selection on Morphology of Cliff Swallows Is Driven by Climate

The extent to which fluctuating selection can maintain evolutionary stasis in most populations remains an unresolved question in evolutionary biology. Climate has been hypothesized to drive reversals in the direction of selection among different time periods and may also be responsible for intense episodic selection caused by rare weather events. We measured viability selection associated with morphological traits in cliff swallows (Petrochelidon pyrrhonota) in western Nebraska, USA, over a 14-year period following a rare climatic event. We used mark-recapture to estimate the annual apparent survival of over 26 000 individuals whose wing, tail, tarsus, and bill had been measured. The fitness functions associated with tarsus length and bill dimensions fluctuated depending on annual climate conditions on the birds’ breeding grounds. The oscillating yearly patterns may have slowed and occasionally reversed directional change in trait trajectories, although there was a trend over time for all traits except tarsus to increase in size. The net positive directional selection on some traits, despite periodic climate-associated fluctuations, suggests that cliff swallow morphology in the population is likely to keep changing and supports recent work contending that selection in general does not fluctuate enough to be an effective driver of stasis

Plant defense against herbivorous pests:exploiting resistance and tolerance traits for sustainable crop protection

Interactions between plants and insect herbivores are important determinants of plant productivity in managed and natural vegetation. In response to attack, plants have evolved a range of defenses to reduce the threat of injury and loss of productivity. Crop losses from damage caused by arthropod pests can exceed 15% annually. Crop domestication and selection for improved yield and quality can alter the defensive capability of the crop, increasing reliance on artificial crop protection. Sustainable agriculture, however, depends on reduced chemical inputs. There is an urgent need, therefore, to identify plant defensive traits for crop improvement. Plant defense can be divided into resistance and tolerance strategies. Plant traits that confer herbivore resistance typically prevent or reduce herbivore damage through expression of traits that deter pests from settling, attaching to surfaces, feeding and reproducing, or that reduce palatability. Plant tolerance of herbivory involves expression of traits that limit the negative impact of herbivore damage on productivity and yield. Identifying the defensive traits expressed by plants to deter herbivores or limit herbivore damage, and understanding the underlying defense mechanisms, is crucial for crop scientists to exploit plant defensive traits in crop breeding. In this review, we assess the traits and mechanisms underpinning herbivore resistance and tolerance, and conclude that physical defense traits, plant vigor and herbivore-induced plant volatiles show considerable utility in pest control, along with mixed species crops. We highlight emerging approaches for accelerating the identification of plant defensive traits and facilitating their deployment to improve the future sustainability of crop protection

Phenomenon-based research in management and organisation science: When is it rigorous and does it matter?

Recently, the editors of Long Range Planning called for more phenomenon-based research. Such research focuses on identifying and reporting on new or recent phenomena of interest and relevance to management and organisation science. In this article, we explore the nature of phenomenon-based research and develop a research strategy that provides guidelines for researchers seeking to make this type of scientific inquiry rigorous and relevant. Phenomenon-based research establishes and describes the empirical facts and constructs that enable scientific inquiry to proceed. An account of the study of open source software development illustrates the research strategy. Rigorous phenomenon-based research tackles problems that are relevant to management practice and fall outside the scope of available theories. Phenomenon-based research also bridges epistemological and disciplinary divides because it unites diverse scholars around their shared interest in the phenomenon and their joint engagement in the research activities: identification, exploration, design, theorising and synthesis